Often, you hear NFL analysts say they think a team will do well because they've won 4 of their last 5 at home against this week's opponent. Or that a player will have a tough day because the opposing defense has only allowed one 80-yard rusher and one rushing touchdown over the last four weeks. It seems sensible enough, but how do we know that these stats carry any predictive weight?
Has there been a study done that if a team does well against the run in four or more of its past five games then it's likely to play good run defense in a sixth game? If so, how often does the sixth game correspond to four of the past five and not the one where the opponent did run successfully?
At some point, we ascribe some kind of causation to repeated correlations - we assume, for example, that the Giants are a good running team, or that the Ravens are a good run defense. But how much it takes before we're convinced of that, and how much you can read into shorter bursts of team success is unclear.
On the flip side, you don't want to wait until a team does something 10 games in a row before you belatedly buy in. You have to be both skeptical and opportunistic at the same time - you doubt that it means anything, but you're also on the lookout for meaningful performances even in a short sample - and you have to hope you can tell the difference.
In the NFL it's particularly hard because sometimes team cohesion can pick up for a game or two, then fall apart - and we don't know the reasons. Putting past performance into proper context is hard, so there's no short answer for how to do it. But I'm fairly convinced that hanging your hat on a bunch of recent stats (without considering a myriad of contextual factors) will lead you astray more often than not, i.e., a little knowledge is dangerous.